is 2500-3 (1995): sampling inspection procedures, part 3:...

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IS 2500-3 (1995): Sampling Inspection Procedures, Part 3:Attribute Sampling Plans Indexed by Limiting Quality (LQ)for Isolated Lot Inspection [MSD 3: Statistical Methods forQuality and Reliability]

IS 2500 (Part 3) : 1995 IS0 2859-2 : 1985

Indian Standard

SAMPLING INSPECTION PROCEDURES PART 3 ATTRIBUTE SAMPLING PLANS INDEXED BY LIMITING QUALITY ( LQ) FOR

ISOLATED LOT INSPECTION

IS0 Title : Sampling procedures for inspection by attributes - Part 2 : Sampling

pians indexed by limiting quality ( LQ ) for isolated lot inspection ]

( First Reprint JULY 1997 )

ICS .No. 03.120.10

0 BIS 1995

BUREAU OF INDIAN STANDARDS MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

October 1995 Price Group 9

Statistical Methods for Quality and Reliability Sectional Committee, MSD 3

NATIONAL FOREWORD

This Indian Standard which is identical with IS0 2859-2 : 1985 ‘Sampling procedures for inspection by attributes - Part 2 : Sampling plans indexed by limiting quality ( LQ ) for isolated lot inspection’, issued by the International Organization for Standardization ( IS0 ), was adopted by the Bureau of Indian Standards on the recommendation of the Statistical. Methods for Quality and Reliability Sectional Committee ( MSD 3 ), and approval of the Management and Systems Division Council.

This standard ( Part 3 ) is third in the series of Sampling Inspection Procedures. The other published parts are as follows:

Part 1 Attribute sampling plans indexed by acceptable quality level ( AQL ) for lot-by-lot inspection

Part 2 Inspection by variables for percent defective

The text of IS0 2859-2 : 1985 has been approved as suitable for publication as Indian Standard without deviations. Certain conventions are, however, not identical to those used in Indian Standards. Attention is particularly drawn to the following:

a) Wherever the words ‘this part of IS0 2859’ appear referring to this standard, they should be read as ‘this part of IS 2500’.

b) Comma (J has been used as decimal marker while in Indian Standards the current practice is to use a point (.) as the decimal marker.

In the adopted standard, informative reference appears to IS0 2859/i ‘Sampling procedures for inspection by attributes -- Part 1: Sampling plans indexed by acceptable quality level ( AQL ) for lot-by- lot inspection’ which has been adopted in foto as IS 2500 ( Part 1 ) : 1992 ‘Sampling inspection procedures: Part 1 Attribute sampling plans indexed by acceptable quality level ( AQL ) for lot-by-lot inspection’.

IS 2500 (Part 3) : 1995

IS0 2859-2 : 1992

Indian Standard

SAMPLING INSPECTION PROCEDURES PART 3 ATTRIBUTE SAMPLING PLANS INDEXED BY LIMITING QUALITY ( LQ ) FOR

ISOLATED LOT INSPECTION

0 Introduction

0.1 General

IS0 2859 comprises four parts:

Part 0: General introduction.

Part 1 : Sampling plans indexed by acceptable quality level

IAQL) for lot-by-lot inspection.

Part 2: Sampling plans indexed by limiting quality (LO) for

isolated lot inspection.

Part 3: Skip lot sampling plan.

IS0 2859/l sampling plans, indexed in terms of AQL, which is

defined as a process average, were primarily designed for the

assessment of a continuing series of lots. This enables

switchingrules to be employed which not only give protection to the consumer (by the switch to tightened inspection and

discontinuation where necessary) but also provide an incentive

to the producer Iby the switch to reduced inspection) with a

reduction to test and inspection costs (when consistently good

quality is achieved). However, there is little doubt that in many industrial situations today the switching rules are not applied

for a variety of reasons or excuses, not all of which may be

valid :

a) individual IS0 2859/l plans are used alone but “AQL”

protection is still claimed or AQL re-defined, to suit “SO- c&x! unique products”;

b) “our industry.. product is specia! so IS0 285911 standard plans need not apply to us”;

c) production is intermittent (not continuous);

d) production is from several different sources in varying

quantities, i.e. “job lots”;

e) purchases are from stock-holders - no source data

available;

f) lots are “small” (use of hypergeometric distribution re-

quired);

g) lots are “isolated”;

h) lots are resubmitted after initial rejection.

Consequently, in certain of the above cases consumer protec-

tion may need to be attained or measured by other methods.

This part of IS0 2859 uses the limiting quality to measure consumer protection. It should be remembered, however, that

prior information on the supplier’s quality assurance system

and its effectiveness may play a major part in deciding whether

or not to accept a single lot.

0.2 Objectives

In an attempt to reconcile the somewhat diverse requests for

assistance made over the past few years by committees of international standardizing bodies representing various product

sectors, this part of IS0 2859 was drawn up in accordance with

the following principles:

a) the new LQ plans can be easily integrated with the

existing AQL plans in IS0 265911;

b) the LQ indexing uses a preferred series of values that

cannot be confused with the preferred series of AQL values;

c) the five basic numbers associated with a single sampl-

ing plan, i.e. lot size, sample size, acceptance number, AQL

(or quality accepted with probability 0,95) and LQ, appear in

the same table, whenever possible.

0.3 Summary

The problems associated with acceptance sampiing inspection involve defining unambiguously the criteria used to judge discrete individual items supplied in quantity, the quality level

expected from the manufacturing process, the discrimination

offered by the plans and the procedure to be followed when a lot is not accepted. Above all, however, it is necessary to design the sampling scheme so that it may easily be invoked in

a purchasing contract. The plans in this part of IS0 2859 make

maximum use of the established plans given in IS0 2859/l, so that sub-clause 12.6 of IS0 2859/l (see 1.1) can be made

directly operational, by providing a rationalized series of plans

indexed in terms of limiting quality (LQ).

1

IS 25.00 (Part 3) : 1995

IS0 2859.2 : 1992

1 Scope and field of application

;.l Scope

This part of IS0 2859 establishes LQ sampling plans and procedures for inspection by attributes compatible with IS0 2859/l

that can be used when the switching rules given in IS0

2B59/lare not applied, for example, when lots are of an isolated

nature.

The plans in this part of IS0 2859 are indexed by a preferred

series of limiting qualities (LO) with a consumer’s risk usually below 10 %, but always below 13 %. This method of indexing permits the “ad-hoc” proceduret) mentioned in sub-clause

12.6 of IS0 2859/l to be implemented as a standard procedure.

NOTE - The plans in IS0 2859/l are indexed by a preferred series of AQL values and inspection levels. During the inspection of a continuing series of lots the application of switching rules helps to ensure that the process average in that series of lots is kept below the specified AQL. Limiting quality does not have the same direct relationship with the process average (see 3.5.1 I.

1.2 Field of application

Alternative procedures are provided in this part of IS0 2859 to

cater for two situations often met in practice:

2

a) Procedure A, to be used when the supplier and con-

sumer both wish to regard ?he lot in isolation. The tables are based on random sampling from finite lots for both con-

sumer and producer risks. This procedure shall be used

unless there is a specific instruction to use procedure 8.

b) Procedure 8, to be used when the supplier regards the

lot as one of continuing series but the consumer considers the lot received in isolation. The tables are based on random

sampling from a finite lot for consumer’s risk at the limiting

quality, but random sampling from a process for the producer’s risk and the tabulated values of the operating

characteristic (OC) curves. The plans used are a selection of

the plans available in IS0 2859/l so that a producer can

maintain consistent procedures for customers whether or

not they receive individual lots or a continuing series of lots. This procedure is suitable for inclusion in product standards

or specifications that contain sampling clauses. The

manufacturer will be concerned withall of his production,

but the individual consumer only with the particularlot received.

Definitions

The definitions given in IS0 2859/l shall apply.

3 Choice of sampling plan

3.1 Specifying a sampling plan

When reference is made to this part of IS0 2859 in a contract or specification, it is necessary to specify the procedure to be

used (i.e. either A or Pr. In the absence of any reference to either procedure, then procedure A shall be used.

3.2 Choice of sampling procedure

Although procedure A is based on the hypergeometric distribu-

tion for sampling results, this distribution is well approximated

by the binomial distribution for plans with non-zero acceptance

numbers in procedure A. Hence the OC curves for these plans

are well approximated by the tabulated performance of the

same plans in procedure B. However, procedure A uses plans

with acceptance number zero and with sample sizes based on the hypergeometric distribution of sampling results while pro-

cedure B excludes accept zero plans, replacing them with

106 % inspection.

The choice between the procedures is dominated by the at-

titude towards accept zero plans. Procedure A uses accept zero

plans linking the sample size and the lot size by the

hypergeometric distribution until the proposed plan cor- responds to the accept zero plan in IS0 2859/l corresponding

to that limiting quality. Thereafter the progression of sampling

size and acceptance number with lot size is based on the in-

spection levels available in IS0 2859/l. The overall effect of

procedure A resembles inspection level II for limiting quality

less than 8 % and level I for limiting quality greater than 8 %

with 8 % being intermediate between these levels.

Procedure B provides greater flexibility in the choice of inspec-

tion levels. The tabulated OC curves are based on the prob-

ability of producing a nonconforming unit so they are approxi-

mately correct for small sampling fractions but as the sampling fraction increases the curves (and tables) underestimate the

probability of acceptance for good quality and underestimate

the probability of rejection for poor quality. For sufficiently

small lots, procedure B requires 100 % inspection.

Both procedures treat the limiting quality (LO) as the actual

percent nonconforming units in the submitted lots and the

probability of acc’eptance at this limiting quality can be found in

table Dl for procedure A and tables Bl to BlO for procedure B. Procedure B is indicated as the appropriate procedure if the

manufacturer is concerned with a continuing series of lots;

whether or not these go to the same consumer. Procedure A is

indicated as the appropriate procedure when the lot is a single lot and shall be used if accept zero plans are required to be part

of the sampling scheme.

3.3 Procedure A (use table A)

A plan is identified by the lot size and the limiting quality (LQ).

With the specified lot size and limiting quality as indexing

values, the sampling size (n) and acceptance number (AC) are

given in table A.

1) IS0 2859/l sub-clause 12.6.2, states: “If the lot or batch is OT an isolated nature, it may be desirable to limit the selection of sampling plans to those, associated with a designated AQL value, that provide not less than a specified limiting quality protection. Sampling plans for this purpose can be selected by choosing a limiting quality (LO) and a consumer’s risk to be associated with it. Tables 6 and 7 give process levels for which the probabilities of lot acceptance under various sampling plans are 10 % and 5 %, respectively.” This part of IS0 2859 establishes preferred values for the LQ and allows the consumer’s risk tc vary as indicated above.

2

Although the primary index to these tables is the limiting quality

(LQ), the producer/supplier needs guidance on the quality level required if lots are to have a high probability of acceptance. In-

formation on the producer’s risk point is contained in table Dl. Information on the probability of acceptance of relatively good

lots by accept zero plans is given in table D2.

3.4 Procedure B (use tables B)

A plan is identified by the lot size, limiting quality (LQ) and the inspection level (unless otherwise specified, level II shall be

used).

The specified limiting quality is used to select the appropriate

table from tables Bl to B10. Within each table the specified lot

size and inspection level indicate the appropriate sample size

(n) and acceptance number (AC). Although the primary index

to the table is the limiting quality (LQ), the producer/supplier

needs guidance on the quality level required if lots are to have a

high probability of acceptance. Each table gives information on

the equivalent AQL and details of the OC curves. The OC

curves are indexed by the sample size code letter used in

IS0 285911 and the acceptance number.

The OC curves given under tables Bl to BIO are based on the

Poisson/binomial distribution; the actual operating charac-

teristic will be more discriminating than these curves by accepting with greater probability when the indicated probability

is > 0,90 and with a smaller probability when the indicated

probability is < 0,lO.

3.5 Choice of parameters for the sampling

procedures

3.5.1 Limiting quality (LQI

Unlike the AQL, which provides a guide for the producer on the

level or quality he needs to produce so that he can satisfy the

acceptance criteria (sampling clause) most of the time, the limiting quality does not provide a reliable guide for the con-

sumer as to the true quality of the accepted lots. For this reason the limiting quality should be chosen realistically at a minimum

of three times the desired quality.

This enables the producer/supplier to provide lots of the

desired quality and still have a reasonable probability of accep-

tance for the submitted lots, at least for acceptance numbers 3,

5, 10 and 18. For acceptance number 1 plans the lots have to

have a quality better than LQ,, and for acceptance number zero plans the lots have to be perfect or nearly perfect before the

probability of acceptance rises to 0,95 or greater. The limiting

values are restricted to a set of preferred values and the plans are intended to be used with these preferred values. If these

plans are introduced where a non-standard limiting quality is

already specified, the plans should be entered with the preferred value (LO) corresponding to the interval containing the

non-standard value (L) listed in column 4 of table C. Columns 2

and 3 of table C contain information on the consumer’s risk qualities (CRQ) found in tables Bl to BlO for consumer’s risks

of 10 % and 5 %.

IS 2500 (Part 3) : 1995

IS0 2859-2 : 1992

.

Example:

The limiting quality has previously been set at 3.5 %. This is not a preferred value and the tables shall be entered by using the nominal limiting quality LQ = 3,15 % since

3,5 % lies in the range 2,5 % < LO <4,0 %.

3.5.2 Inspection level

In the IS0 2859/l procedures, increased sample size cor- responds to a greater protection for the consumer. In this part

of IS0 2859, consumer protection is held approximately cons-

tant and the effect of increasing sample size is to permit the

supplier greater latitude in the permitted process averages. If

the consumer is satisfied by the protection provided against an

occasional poor lot by the nominal limiting quality, then the in-

spection level is primarily of interest to the supplier, especially if

the costs of the sampling inspection are borne by him. A pro-

cess average well below the limiting quality (better quality)

would allow the use of smaller sample sizes. Conversely, if the

consumer is concerned with actual rather than limiting quality,

or if he pays for the sampling costs, then greater inspection levels are not necessarily advantageous. For this reason, in-

spection level III provided by IS0 2859/l has not been incor- porated in this part of IS0 2859 for limiting qualities greater

than 5 %. When sampie sizes have to be kept small and other

considerations are secondary, specifying level S-2 has the effect of providing a fixed sample size for all lot sizes, the sample

size depending only on the limiting quality.

4 Rules for acceptance and non-acceptance

4.1 Sampling

Once the sampling plan has been determined as in clause 3, the

specified sample units shall now be drawn at random from the lot, and all units in the sample inspected.

4.2 Acceptance

If the number of nonconforming units, or the total number of

nonconformities, found in the sample is equal to or less than the acceptance number (AC) specified in the plan, the lot shall be accepted.

4.3 Nonconforming units

Notwithstanding that the lot is accepted, any nonconforming

units found during inspection, whether forming part of the

sample or not, shall be rejected.

4.4 Non-acceptance and resubmission

If the number of nonconforming units found in the sample is

greater than the acceptance number (AC), the lot is unaccep-

table. An unacceptable lot may not be resubmitted for inspection unless

a) the Responsible Autho* agrees, and

b) all units in the lot have been re-examined or retested

and all nonconforming units have been removed or replaced

by good units or nonconformities have been corrected.

3

IS 2500 (Part 3) : 1995

IS0 2859-2 : 1992

If the Responsible Authority agrees to the resubmission of an

unacceptable lot, he shall determine the method of acceptance inspection to be applied (i.e. LO and/or inspection level) and

whether re-inspection shall include all types or classes of nonconformities or only those that caused the initial rejection.

5 Double and multiple sampling plans

Tables D3 and D4 provide the sample sizes and acceptance pat-

terns for the double and multiple sampling plans in IS0 2859/l

equivalent to the single sampling plans given in tables 61 to 810. The sample size code agrees with that in IS0 285911 and

the acceptance pattern code is the acceptance number in the

corresponding’single size plans. Since procedure A and pro-

cedure B plans have similar OC curves for non-zero acceptance

numbers, these double and multiple plans can also be used in

procedure A to replace the corresponding single sampling plan. The user is referred to 11.1.2 and 11.1.3 in IS0 2859/l for the

operation of these double and multiple sampling plans.

6 Examples illustrating how to use this part of IS0 2659

6.1 A consumer wishes to purchase prepacked sets of 10

screws to include in the self-assembly bookcase kits he plans to

sell. While he prefers each set to contain exactly 10 screws, he

can tolerate 1 % of packs with fewer screws but he does not

want to risk accepting a much higher percentage of deficient packs. He plans to produce 5 000 kits in lots of 1 250.

The supplier agrees to use procedure A with nominal limiting

quality 3.15 %. For lots of size 1 250, the selected plan has n = 125, AC = 1.

The supplier offers to provide the packs needed for all 5 000 kits

as a single lot. The new sampling plan has n = 200, AC = 3.

The single lot requires proportionately fewer tested items and yet the sampling plan still provides a high probability of rejec-

tion for quality as poor as 3,15 %, while increasing the prob-

ability of acceptance for a lot of quality 1 % from O&l to 088.

6.2 The same consumer wishes to purchase the wooden

components of his self-assembly bookcase kit as standard-size,

plastic-faced chipboard panels. The supplier produces these panels as part of his regular production and regards the 7 500

panels needed for each lot of 1 250 kits as single lots in the

general stream of supply to DIY shops. Scars to the plastic

facing occur with probability 0,025 according to quality control checks. The consumer can tolerate some scarred panels since

these can be detected and set aside during the processing to

.

produce the bookcase kit, but he decides that if 5 % of the panels were scarred this would present problems during the

processing.

The consumer and supplier agree that procedure B is ap-

propriate and select nominal limiting quality 5,0 % with inspec-

tion level S-4. The parameters of the sampling plan for a lot size

of 7 500 is n = 80, AC = 1. With this plan the probability of

acceptance with the current process average is less than 0,5. A

lot which is unacceptable has to be 100 % inspected before use

and this high probability of non-acceptance implies inspection

costs larger than desirable.

Inspection level III would have provided a sampling plan with

n = 315 and AC = 10. The current process average would

produce lots with a probability of acceptance greater than 080.

A supplier with a better process average, say 1 %, would ob-

tain a similar probability of acceptance with inspection level

S-4. This illustrates the ability of better suppliers to work with

smaller sample sizes whilst still meeting the same limiting qual-

ity criterion.

7 Compatibility with IS0 2659/l

7.1 General

Within the probability constraints inherent in attribute sam-

pling, the LQ indexed plans standardized in table A and

tables B provide a rationalized selection from the existing AQL

indexed plans of IS0 2859/l. Similar rules for acceptance and

non-acceptance and the IS0 2859/l lot size categories have

also been retained for compatibility. Significant deviations are

given in 7.2 and 7.3.

7.2 Procedure A (see table A)

For unique lots with a relatively high sample size/lot size ratio,

it becomes necessary to use the hypergeometric distribution. Consequently, there are an additional 39 (AC = 0) plans in

table A for which operating characteristic (OCI curve data is

given in table D2. The remaining 80 plans of table A have been taken from IS0 285911.

7.3 Procedure B (see tables B)

All the plans in tables B have been selected from IS0 2859/l by using a sliding scale for the consumer’s risk (usually below

10 %) at the specified limiting quality (LO). IS0 2859/l inspec-

tion levels are also included (see 3.5.2) but AC = 0 plans have not been included in tables B, as table A can be used, if

AC = 0 plans are considered essential.

4

IS 2500 (Part 3) : 1995

IS0 2859-2 : 1992

.

Table A - Single sampling plans indexed by limiting quality (LQ) (Procedure A)

Limiting quality in percent (LQ) Lot size 0.5 0,8 1.25 2.0 3,15 5.0 8,O 12,5 20 32

n 25" 17" 13 9 6 16to 25

AC + + + +

0 0 0 0 0

n 50" 50" 28" 22 15 10 6 26to 60 + + + AC 0 0 0 0 0 0 0

51to 90

" 90" 50 44 34 24 16 10 8 + -+ AC 0 0 0 0 0 0 0 0

" 150" 90 80 55 38 26 18 13 13 91 to 150 AC 0 0 0 0 0 0 0 0 1

n 200" 170" 130 95 65 42 28 20 20 13 151 to 280 AC 0 0 0 0 0 0 0 0 1 1

n 280 220 155 105 80 50 32 32 20 20 281to 500 AC 0 0 0 0 0 0 0 1 1 3

n 380 255 170 125 125 80 50 32 32 32 501 to 1200 AC 0 0 0 0 1 1 1 1 3 5

1201to 3200 n 430 280 200 200 125 125 80 50 50 50 AC 0 0 0 1 1 3 3 3 5 10

n 450 315 315 200 200 200 125 80 80 80 3201to 10000 AC 0 0 1 1 3 5 5 5 10 18

10001 to 35000 n 500 500 315 315 315 315 200 125 125 80

AC 0 1 1 3 5 10 10 10 18 18

35001 to150000 ” 800 500 500 500 500 500 315 200 125 80

AC 1 1 3 5 10 18 18 18 18 18

150001 to500000 n 800 800 800 800 800 500 315 200 125 80

AC 1 3 5 10 18 18 18 18 18 18

> 500000 n 1250 1250 1 250 1250 500 500 315 200 125 80

AC 3 5 10 18 18 18 18 18 18 18

1) When n exceeds the lot size, use 100 % inspection with zero acceptance number.

+ Limiting quality implies less than one nonconforming item in the lot. Use first available plan for higher LQ.

5

Table Bl - Sampling plans for limiting quality 0.5 %

IS0 2859/l Tabulated values of submitted quality Acceptance

Lot sizes for inspection levels Single sampling plan Code letter accepted with designated probabilities’) probabilities for

(Normal inspection) (quality as percent nonconforming) limiting

quality21

S-l to s-3 s-4 I II III AQL n AC 0,95 0.90 050 0,lO 0,05 max. min.

> 80031 > 8003’ > 8003) 8013’ to 500 OOCI 8013) to 150 000 0,065 800 1 P 0,044 4 0,066 5 0,210 0,486 0,593 0,091 0,000

>500000 150 001

to

500006 0.10 1250 3 Q 0,109 0,140 0,294 0,534 0,620 0,129 0,129

>5OOOCO 0,lO 2600 5 R 0,131 0,158 0,284 0,464 0,526 0,966 0,666

1) Probability calculated by the Poisson approximation.

2) The exact acceptance probabilities calculated from the hypergeometric distribution vary with lot size, the maximum and minimum values attained for permitted lot sizes are given for each plan.

31 For fewer than 801 in the lot, 100 % inspect the lot.

Operating characteristic curves for single sampling plans

0 (Curves are identified by sample size code)

0,2 O/L 0,6 0,8

0.8

0,2 0,C 0,6 0,8

Quality of submitted lots (percent nonconforming)

Table &? - Single sampling plans for limiting quality 0,8 %

0.10 I 0,05 I max. j min.

IS0 285911 Tabulated values of submitted quality Acceptance

Lot sizes for inspection levels Single sampling plan Code letter accepted with designated probabilities11 probabilities

INormal inspection) (quality as percent nonconforming) for limiting

quality*’

s-1 to s-3 s-4 I II III AQL n AC 0,95 0.90 0.50

> 50031 > 50031 5013) 5013’ 501 3’

to to

150000 ot?l o,1c6 - o,336_

>500000

I Ti

150 001

to

500000 ) 0,171 1 0,218 / 0,459

0,778 0,949 0,091 0,000

I 1 I I

>500000 >15oooo 0.15 1250 5 Q 0,209 0,252 1 0,454

1 Probability calculated by the Poisson approximation.

0,835 0,969 0,118 0,115

0,742 0,841 0,066 0,066

21 The exact acceptance probabilities calculated from the hypergeometric distribution vary with lot size, the maximum and minimum values attained for permitted lot sizes are given for each plan.

3) For fewer than 501 in the lot, 100 % inspect the lot.


-J (Curves are identified by sample size code)

Quality of submitted lots lpercent nonconforming)

Table 83 - Single sampling plans for limiting quality 1.25 %

IS0 285Wl Lot sizes for inspection levels Single sampling plan

(Normal inspection)

S-l t3 s, -

s-4 ----II

III AQL n AC

>31531 j >31531 3163’ 3163’ 31631

I It0 to / to

,,1,~1 150001 1 35 001

to 5ooouo

>500000

1) Probability calculated by the Poisson approximation.

Code letter

Tabulated values of submitted quality

accepted with designated probabilitiesl’

(quality as percent nonconforming)

Acceptance

probabilities for limiting

quality2)

0.95 0.90 09 0.10 1

0.05 max.

M 1.23 / 1,51 0,095

N 1.34 1.55 0,129

P 0,327 0,394 0,709 1,16 1,31 0.066

Q 0,494 0,562 0,853 1.23 1,36 0,089

___ min.

0.~

0,122

0.064

0.089

2) The exact acceptance probabilities calculated from the hypergeometric distribution vary with lot size, the maximum and minimum values attained for permitted lot sizes are given for each plan



(Curves are identified by sample size code)

0.6


Tal+ 84 - Single sampling plans for limiting quality 2.00 %

IS0 2959/l Single sampling plan

(Normal inspection) Code letter

Tabulated values of submitted quality accepted with designated probabilities’)


Acceptance probabilities for

limiting

quality”

Lot sizes for inspection levels

sl:,:,:r:,s AQL 1 n AC 0,95 s-4 I II III

> 20031 20131 20131 2013’

1) Proba

to 15OOQO

to 3200

3 201

to

10 CQO

to 10 oocl

10001 -

to 35 000

1 L 0,178

0,433

1 t --/

0,533 1,17 2.12 2,46 0,124 0,111

0,630 1,13 1,86 2.10 0,065 0,061

0,878 1.33 1,93 2.12 0,075 0,073

150 001

to

5OQOOiI 3 M

~-@j ;ljzz 1 ;ilI ity calculated by the Poisson approximation.

N 0,523

0,771 P i



W



0.8

O,L

012

3

1,o 2,0 3.0 L.0


Table 87 - Single sampling plans for limiting quality 8.0 % ETii

Lot sizes for inspection levels IS0 2858/l

Single sampling plan (Normal inspection1

Tabulated values uf submitted quality accepted with designated probabilities’)


H 0,712 1.07 3.33 756 9.13 0,083 0,000

J 1.73 2.20 4,57 8,16 939 0,109 0,090

K 269 2,52 454 7.42 8.41 0,059 0,051

L 3.09 3.51 533 7.70 8.48 0,069 0,064

) Probability calculated by the Poisson approximation for code letters K and L. Binomial distribl an for code letters H and J.


31 For fewer than 51 in the lot, 100 % inspect the lot.

Opera’ting characteristic curves for single sampling plans

(Curves are identified by sainpie size code)

0,6


Table 88 - Single sampling plans for limiting quality 12,5 %

S-1 to s-:

> 323’

IS0 2869/l Lot sizes for inspection levels single sampling plan Code letter

lcontrale normal) _____-

s-4 I II III AQL n Ac-

3331 333) 333! 333’

to to to to

5OOOQO 10 ooo 12lxl 280 1,5 32 1 G

~5OOooo 10001 1 201 281

to to to 35 ooo 3200 500 2,5 50 3 H

35 001 3 201 501

to to to

500000 10 000 1 200 2.5 80 5 J

>500000 >lOooo >1200 4.0 125 10 K

Tabulated values of submitted quality

accepted with designated probabilities11



limiting

qualityz’

0,95 O,W 1 0,50

1.13 1.67 5.19

2,77 3.54 7.30

3.32 3.98 7,M

4.94 5,62 8,53

1) Probability calculated by the Poisson approximation for code letter K. Binomial distribution for code letters G, H and J.



2 Operating characteristic curves for single sampling plans



Table B9 - Single sampling plans for limiting quality 20.0 %

Lot sizes for inspection levels

S-1 to s-3 s-4 I II III

>203’ 213’ 213) 213’ 2131

to to to to

35 ooo 1200 500 150

35 001 1 201 501 151

to to to to

500000 10 000 1206 280

I I />35OOc1 >32Ocl >500

1 I Probability calculated by the binomial distribution.

IS0 286!l/l Single sampling plan (Normal inspection)

AQL n AC

Code letter

2.5 20 1 F

4,O 32 3 G

4.0 50 5 H

6,5 80 10 J


z Operating characteristic curves for single sampling plans


1,o

0,6

Tabulated values of submitted quality accepted with designated probabilities”


0,95 0.90 0.50 0,lO WJ5


limiting quality*)

max. min.

160 269 8,25 18,l 21.6 0,069 0,000

4.39 556 11.4 19.7 22.5 0,093 0,072

5.34 6.42 11.3 17.8 19.9 0,046 0,037

7.91 8.95 13.3 18.6 20.3 0,066 0,049

2) The exact acceptance probabilities calculated from the hypergeometric distribution vary with lot size, the maximum and minimum values attainedfor permitted lot sizes are given for each plan.


Table BlO - Single sampling plans for limiting quality 32.0 %

Lot sizes for inspection levels IS0 2859/l

Single sampling plan

(Normal inspection) Code letter

Tabulated values of submitted quality accepted with designated probabilities”



limiting

quality*) \

S-l to s-3 S-4 I II Ill AQL II AC 095 0.90 0.50 0.10 0.05 max. min.

> 133’ 143’ 143’ 1431 143)

to to to to

3Mo 500 280 90 4.0 13 1 E 2.81 4.16 12.6 26,8 31.6 0,047 0,000

3201 501 281 91

to to to to

35000 1200 500 156 6.5 20 3 F 7.13 9.03 18.1 30.4 34.4 0,077 0,062

35 001 1 201 501 151

to to to to

500000 10 000 1200 280 6.5 32 5 G 8.5 10,2 17.5 27,l 30,l 0,031 0,022

>5OOooo >lOOOO >1200 >280 10.0 50 10 H 12.9 14.5 21.2 29.1 31,6 0,044 0,042

1 I Probability calculated by the binomial distribution.





0,6


IS 2500 (Part 3) : 1995

IS0 2859-2 : 1992

Table C - Relation between limiting quality (LQ) and consumer’s risk quality (CRQ)

Preferred value of limiting quality (LQ)

%

Corresponding range of CRQ in tables Bl to BlO

(at 10 % consumer’s risk)

0,5 0.46 < CRQ < 054

0,8 0.74 < CRQ i 0.84

1.25 1.16 < CRQ < 1.34

2.0 166 < CRQ < 2.12

3.15 2.94 < CRQ < 3.34

5,O 4.64 < CRQ < 5,35

8.0 7.42 < CRQ < 8,16

12.5 11,3 < CRQ < 12.9

20.0 17,8 < CRQ < 19,7

32.0 26.8 < CRQ < 30.4

Corresponding range of CRQ in tables Bl to BlO

(at 5 % consumers risk1

Corresponding interval’) for non-standard value

of limiting quality IL)

0.52 < CRQ < 0.62

0.84 < CRQ < 0,97

1.31 < CRQ < 1,55

2.10 < CRQ < 2,46

334 < CRQ < 3.88

5,26 < CRQ < 6.20

8.41 < CRQ < 9.39

12,7 < CRQ < 14.8

19.9 < CRQ < 22.5

30.1 < CRQ < 34.4

0.4 < L < 0.65

0,65<L< 1,0

1,0 < L < 1.6

1,6 < L < 2.5

2.5 < L < 4,0

4.0 < L < 6.5

6.5 < L < 10.0

10,o < L < 15,0

15,0 < L < 25,5

25,0 < L < 40,O

1) These plans are intende o be used with the preterred sehes of limlttng qualltres. If these plans are Introduced where a non-standard limiting

quality is already specified, the plans should be entered with the preferred value (LQ) corresponding to the interval containing the non-standard

value (Ll.

16

Table Dl .- Summary oi sampling plan properties for procedure A

Sample size/acceptance No. (~/AC) Probability of acceptance at the limiting quality 1) (PLQ)

Percent nonconforming (p) Probability of acceptance at quality (p)

Each cell in the table shows the consumer’s risk (PLQ) and the droducer’s risk point (p, P,).

51

151 to 293 Inspect 170/o 0,102 130/O 0,095 95/o 0,069 65/O 0.090 42/O 0,097 28/O 0.0% 20/O 0,062 20/l 0.062 1311 0.044 every item 0 1.0 0 1.0 0 1.0 0 1.0 0 1.0 0 1.0 0 1.0 1.79 0.96 296 0.96

26ttom y/o y,y y0 ;y A5670 yl implo y$92 r/o 0061 l'. 50/O 0067 l'.

32/o 0066 l'. 3211 0,071 20/l 0.065 Ml3 0.072 o o 1 o. 0.97 166 0.95 7.20 0.95

31to1200 380/O 0.101 256/o 0,098 im/o 0.100 125/O 0,069 12511 0,061 @J/l 0,079 50/l 0,078 32/l 0,075 3213 0.090 3215 0,029 o 1.0 0 1.0 0 1.0 0 1.0 0,250 0.97 0,417 0.96 0,667 0.96 1.06 0.95 4.42 0.95 8.50 0.95

12cnto 430/o 0,099 260/O 0,635 2WO 0,074 MO/l 0.083 12511 0,088 12513 0,119 69/3 0,106 5013 0,112 5015 0,047 50/10 0,042 3203 0 1.0 0 1.0 0 1.0 0,188 0.95 0,281 0.95 1.13 0.95 1.75 0.95 2,76 0.95 538 0.95 12.9 0.95

3201to 450/o 0,059 315/o 0,076 315/l 0,091 200/l 0.697 200/3 0,120 2cKr/5 0,061 125/5 0,056 8015 0,056 80110 0,056 80/18 0,041

10000 0,010 0.96 0,010 0.97 0,110 0.96 0,180 0.95 0,690 0.95 1.32 0.95 2.12 0.95 332 0.95 7.92 0.95 16.1 0.95

10 001 to 500/o o.OKJ 500/l 0,069 315/l 0,094 31513 0,123 315/5 0,066 315/10 0,080 2al/lO 0,069 125,'lO 0,077 125/18 0,069 60118 0,041

35000 0,009 0.96 0,071 0.95 0,111 0.95 0,437 0.95 0,834 0.95 1.97 0.95 399 0.95 5.01 0.95 10.2 0.95 16.1 0.95

36001to 800/l 0,090 500/l 0,090 50013 0,128 500/5 0,665 500/10 0,083 500118 0,086 315/18 0,077 260/18 0,078 125118 0,069 80/18 0.04~ 150000 0,044 0.95 0,071 0.95 0,273 0.95 0,524 0.95 1.23 095 2.50 0.95 3.99 096 6,31 0% lo,2 0.95 16.1 0.95

156cQ1to am/l 0,091 80013 0,118 609/5 0,060 &Xl/10 0,075 800118 0,062 500/18 0,096 315118 0,077 266118 0,078 125118 0,069 80/18 0.041

500 WO 0,044 095 0,170 0.96 0,328 0.95 0,771 0.95 1.56 0.95 2,x 0.95 399 0.95 6.31 0.95 10.2 0.95 16.1 0.95 ____~

>500000 1250/3 0,129 1250/5 0,066 1250/10 0.089 1250/18 0,090 800118 0,082 503/18 0.086 315/18 0,077 2@3/18 0,078 125/18 0,069 60118 0,041 0,109 0.95 0,209 0,s 0,494 0.95 1.00 0.95 1.56 0.95 2.50 0.95 399 0.95 6.31 0.95 10.2 0.95 16.1 0.95

1

1) Thestated probabilityofacceptanceisthe maximumforlotsoflimiting qualityinthesize rangeandthe minimumforlotswith percent nonconforming p. These probabilities are based on the

hypergeometric distribution. The producer’s risk is (p, PJ, the consumer’s risk point is (LQ. PLQ).

21 No lot in this size range can be of limiting quality since this implies a fractional number of nonconforming.

21 91 to 150 inspect 90/O 80/o 0,099 55/o 0,103 38/O 0,103 26/O 0,092 18/O 0,077 13/o 0.046 13/l 0,041 every it&n 0 1.0 0 1.0 0 1.0 0 1.0 0 1.0 0 1.0 0 1.0 2.67 0.96

-

IS 2500 (Part 3) : 1995

IS0 2859-2 : 1992

Table D2 - Selected hypergeometric data for OC cur&s for zero acceptance plans

A sample of size n is drawn from a lot containing R nonconforming items. The lot is accepted if there are nonconforming items in the

sample (AC = 0). the probability of acceptance for the lot (fs) is shown below for the minimum and maximum lot sizes in the lot size range and the various sampling plans “n/O” (printed in bold type).

Lot size

601 lax

R pa pa 0 1.00 1.00 1 0.24 0.66 2 0.06 0.47 3 0.01 0.32 4 0.00 0.22 5 0.00 0.15 6 0.00 0.10 6 0.00 0.05

430/Q Lot size

1201 32ul

fz pa pa 0 1.00 1.00 1 0.64' 0.67 2 0.41 0.75 3 0.26 0.65 5 0.11 0.49 7 0.04 0.36 16 0.00 0.10 21 0.00 0.05

46010

Lot size

3201 1000

p pa pa 0 1.00 1.M) 1 0.66 0.96 2 0.74 0.91 3 0.63 0.67 15 0.10 0.50 20 0.05 0.40 50 0.00 0.10 65 0.00 0.05

!iOO/O

Lot size

10001 3500

R pa pa 0 1.00 1.00 1 0.95 0.99 2 0.90 0.97 3 0.66 0.93 45 0.10 0.52 58 0.05 0.43 El 0.00 0.10 06 0.00 0.05

W3 1,25 LO 3.15 5.0

125/o

Lot size Lot size Lot size

501 1200

R Pa Pa 0 1.00 1.00 1 0.49 0.79 2 0.24 0.62 3 0,12 0.49 4 0.06 036 5 0.03 0.30 10 0.w 0.09 13 0.w 0.04

501 12a

s pa pa 0 1.00 l.Oc 1 0.66 0.86 2 0.44 0.74 3 0.29 0.63 6 O,ul 0.40 7 0.05 0.34 5 0.00 0.10 9 0.w 0.05

I

1 1

!

1 1 3 4

6

-r-

501 1m

R pa pa 0 l.Gu 1.00 1 0.75 0.90 2 0.56 0.80 3 0.42 0.72 6 0.10 0.41 10 0.05 0.33 20 0.00 0.11 27 0.W 0.05

260/o

Lot size

1201 3200

R Pa Pa 0 1,ccl 1.00 1 0.77 0.91 2 0;59 0.63 3 .0.45 0.76 9 0.09 0.44 11 0.05 0.36 25 0.00 0.10 33 0.00 0.05

315/o

Lot size

3201 1om

R Pa Pa 0 1.00 1.00 1 0.90 0.97 2 0.81 0.94 3 0.73 0.91 22 0.10 0.49 29 0.05 0.39 72 0.00 0.10 93 0.00 0.05

20010

Lot size

12013m

7 pa pa 0 1.00 1.00 1 0.63 0.94 2 0.69 0.m 3 0.56 0.62 3 0.09 0.43 6 0.05 0.36 5 0,Ou 0.10 6 0.W 0.06

am


91 150 91 150 91 150

t pa pa R pa pa R pa pa 0 1.00 1.00 0 1.00 1.00 0 1.00 1.00 1 0.01 0.40 1 0.12 0.47 1 0.40 0.63 2 0.00 0.16 2 0.01 0.22 2 0.15 0.40 3 0.00 0.06 3 0.00 0.10 3 0.06 0.25 4 0.00 0.02 4 0.00 0.05 4 0.02 0.16 5 0.00 0.01 5 0.00 0.02 5 0.01 0.10 6 0.00 0.00 6 0.00 0.01 6 0.00 0.06 7 0.00 0.00 7 0.00 0.00 7 u,Gu 0.04

60/o 44/o 34/Q


51 90 51 90 51 90

R pa pa R pa pa R pa pa 0 1.00 1.00 0 1.00 1.00 0 1.00 1.00 1 0.02 0.44 1 0.14 0.51 1 033 0.62 2 0.00 0.19 2 0.M 0.26 2 0.11 0.36 3 0.00 0.08 3 0.00 0.13 3 0.03 0.24 4 0.00 0.04 4 0.00 0.06 4 0.01 0.14 5 0.00 0.01 5 0.00 0.03 5 0.00 0.09 6 0.00 0.01 6 0.00 0.02 6 0.00 0.05 7 0.00 0.00 7 0.00 0.01 7 0.00 0.03

38/Q

Lot size

91 150

R pa pa 0 1.00 1.00 1 0.56 0.75 2 0;34 ok6 3 0.19 0.41 4 0.11 0.31 5 0.06 0.23 6 0.01 0.09 10 0.00 0.05

Limiting t quality (LQ)

2610

Lot size

26 50

R pa pa 0 1 Ei 2 0:19 3 0.08 4 0.03 6 0.01 s 0.00 7 0.00

8,‘J 12.5

17/Q 13/o

Lot size Lot size

16 25 16 25

R Pa Pa R P, Pa 0 1.00 0 1.00 1.00 1 0.32 1 0.19 0.46 2 0.09 2 0.03 0.22 3 0.02 3 0.00 0.10 4 0.01 4 0.00 0.04

z 0.00 6 5 0.00 0.00 0.01 0.01 7 i.: 7 0.00 0.M)

22/o 15/O

Lot size Lot size

26 50 2% 50

R pa Pa R Pa "a 0 1.00 1.00 0 1.00 1.00 1 0.15 0.56 1 0.42 0.70 2 0.02 0.31 2 0.17 0.49 3 0.00 0.17 3 0.06 0.33 4 0.00 0.09 4 0.02 0.23 5 0.00 0.05 5 0.01 0.15 6 0.00 0.02 6 0.00 0.10 7 0.00 0.01 6 0.00 0.04

24/O 16/O

Lot size Lot size

51 90 51 90

R pa pa R pa pa 0 1.00 1.00 0 1.00 1,oo 1 0.53 0.73 1 0.69 0.62 2 0.26 0.54 2 0.47 0.67 3 0.14 0.39 3 0.31 0.55 4 0.07 0.26 6 0.09 0.30 5 0.03 0.20 6 0.04 0,lS 7 0.01 0.10 11 0.01 0.10 9 0.00 0.05 14 0.00 0.05

26/O 16/O

Lot size Lot size

91 150 91 150

R pa Pa R Pa Pa 0 1.00 1.00 0 1.00 1.00 1 0.71 0.63 1 0.60 0.66 2 0.51 0.66 2 0.64 0.77 3 0.36 0.56 3 0.51 0.66 7 0.09 0.26 10 0.10 0.27 6 0.06 0.21 13 0.w 0.16 12 0.01 0.09 17 0.02 0.10 15 0.00 0.05 27 0.00 0.05

I

Lot size Lot size

16 25 16 25

R Pa Pa R "a Pa 0 1.00 1.00 0 1.00 1.a 1 0.44 0.64 1 0.63 0.71 2 0.16 0.40 3 0.06 0.24

; $;

4 0.02 0.14 4 0:12

;; , :

0.3 5 0.00 0.m 5 0.06 0.z 6 0.00 0.05 7 0.01 0.11 7 0.00 0.02 9 0.00 OS?!

1

10/O 6/O

Lot size Lot size

26 50 26 50

R Pa Pa R Pa Pa 0 1.00 lsm 0 1.00 1.a 1 0.62 0.80 1 0.77 o,tii 2 0.37 0.64 2 0.56 0.7 3 0.22 0.50 3 0.44 0.61 4 0.12 0.40 7 0.12 0.31 6 0.03 0.24 9 0.05 0.a 9 0,Ou 0.11 15 0.00 0.v 12 0.00 0.05 19 0.00 o,o!

IO/O 610

Lot size Lot size

51 90 51 90

R Pa Pa R Pa f'. 0 1.00 1.00 0 1.00 l.ln 1 0.80 0.99 1 0.84 0.9 2 0.64 0.79 2 0.71 0,K 3 0.51 0.70 3 0.59 0.7! 10 0.09 0.29 12 0.10 0.x 12 0.05 0.22 15 0.05 0.2 16 0.01 0.09 22 0.01 O,l( 22 0.00 0.05 27 0.00 O,O!

13/O

Lot size

.Sl 150

R Pa Pa 0 1.00 1.00 1 0.55 0.91 2 0.73 0.63 3 0.63 0.76 14 0.10 0.26 17 0.05 0.20 23 0.02 0.10 30 0.00 0.05

18

IS 2500 (Part 3) : 1995

ISO 2859-2 : 1992

Table D2 - Selected hypergeometric data for OC curves for zero acceptance plans (concluded)

Limiting quality (LQ)

0.5 O,8 1,25 2.0 3,15 5,O 8.0 12,5

17010 130/o 95/O 65/O 42/O 20/O M/O

Lot size Lot size Lot size Lot size Lot size Lot size Lot size

151 260 151 280 151 280 151 2&l 151 280 151 280 151 280

R pa "a R Pa Pa R Pa pa R pa "a R Pa Pa R Pa Pa R f'a Pa

0 1.00 0 1.00 1,oo 0 1.00 1.00 0 1.00 1.00 0 1.00 l,oo 0 l,oo 1,oo 0 1.00 1.00 1 0.33 1 0.14 0.54 1 0.37 0.66 1 0.57 0.77 1 0.72 0.65 1 0.61 0.90 1 0.67 0.93 : 0.15 0.06 2 3 0.02 0.00 0.29 0.15 2 3 0.14 0.06 0.44 0.29 2 3 0.32 0.18 0.45 0.59 2 3 0.52 0.72 2 3 0.66 0.61 2 3 0.75 0.66

0.37 0.61 0.54 0.73 0.65 0.80 4 0.02 4 0,GlJ 0.09 4 0.02 0.19 4 0.10 0.35 7 0.10 0.32 11 0.10 0.31 15 0.11 0.32 5 0.01 5 0.00 0.04 5 0.01 0.12 5 o,ce 0.26 9 0.05 0.23 14 0.05 0.22 20 0.05 0.22 6 0.00 6 0.00 0.02 6 0.00 0.09 9 0.01 0.09 14 0.01 0.10 21 0.01 0,lO 29 0.01 0.10 7 0.00 7 0.00 0.01 7 0.M) 0.05 11 0.00 0.05 18 0,oO 0.05 27 0.00 0,05 36 0,OO 0.05

280/O 220/O 155/o 105/O 80/O 50/O 32/O

Lot size Lot size Lot size Lot size Lot size Lot size Lot size

281 500 261 5al 261 5co 281 500 261 500 261 5cm 261 mo

R pa Pa R Pa P, R Pa Pa R Pa pa R pa Pa R P, Pa R Pa Pa

0 1,al 1.00 0 1.00 1.00 0 l.oo 1.00 0 1.00 1.00 0 1.00 1.00 0 l.oo 1.00 0 1.00 1.00 1 0.00 0.44 1 0.22 0.56 1 0.45 0.69 1 0.63 0.79 1 0.72 0,64 1 0.62 0.90 1 0.69 0.94 2 0,Gu 0.19 2 0.05 0.31 2 0.20 0.46 2 0.39 0.62 2 0.51 0.71 2 0.66 0.61 2 0.76 0.66 3 0,Gu 0.08 3 0.01 0.17 3 0.09 0.33 3 0.24 0.49 3 0.36 0.59 3 0.55 0.73 3 0.69 0.62 4 0.00 0.04 4 OSQ 0.10 4 0.W 0.23 5 0.09 0.31 7 0.09 0.29 12 0.09 0.28 18 0.11 0.30 5 0.00 0.02 5 0.00 0.05 5 0.02 0.15 6 0.06 0.24 9 0.05 0.21 15 0.05 0,20 24 0.05 0.x) 6 0.00 0.01 6 0.00 0.03 6 0.01 0.11 10 0.01 0.09 13 0.01 0.10 21 0.01 0.10 33 0.01 0.10 7 0.00 0.00 7 0.00 0.02 6 0.00 0.05 13 0.00 0.04 17 0.00 0.05 26 0.00 0.05 43 0.00 0.05

20,o 32,0

19

IS 2500 (Part 3) : 1995

IS0 2859-2 : 1992

Table D3 - Equivalent sample sizes for single, double and multiple sampling plans

l- Sample size code letter and cumulative sample sizes 1’ in accordance with IS0 2959/l 1 R

zoo0

1250

2500

560

1 000

1 500

2 000

2500

3000

3 500

1) For double and multiple sampling pians, the tabulated entries are the cumulative sample sizes. In each case the successtve stages ot sampkng take

a fresh sample equal in size to that taken in the first stage. This sample is aggregated with the samples from previous stages and the combined sample

is then tested by the criterion in table 04

Type of

sampling plan E F

13 20

1st 8 13

2nd 16 26

1st 3 5

2nd 6 10

3rd 9 15

4th 12 20

5th 15 25

6th 18 30

7th 21 35 I G

32

20

40 __-

8

16

24

32

40

46

56

H

50

32

64

13

26

39

52

65

78

91

J K L --

M N

80 125 200 -__

125

250

315 500 800 1250

50

100

80

160

200 315

400 630

20 32 50 80 125

40 64 100 160 250

60 96 150 240 375

80 128 200 320 500

100 160 250 406 625

120 192 300 460 750

140 224 350 560 875

Q

800

1600

315

630

945

1 260

1 575

1890

2 205

P

500

1000

200

400

600

800

1 000

1 200

1 400

Single

Double

Multiple

Table D4 - Equivalent acceptance numbers for single, double and multiple sampling plans

Type of sampling plrin

Approximate relative sample sizes

at each stage” n

Single ! 1 18 19 1 2 3 4

0 2 1 4

1 2 4 5

31 2 31 3 3) 2 0 3

0 2 1 4

0 3 2 5

1 3 3 6

1 3 4 6

2 3 6 7

Double I

0,63

0.63

9 14

23 24

I 0.25

0,25

0,25

0,25

0,25

0.25

0.25

Multiple

31 4 0 5 1 8

1 5 3 8 6 12

2 6 6 10 11 17

3 7 8 13 16 22

5 8 11 15 22 25

7 9 14 17 27 29

9 10 18 19 32 33

Discrimination ratio

(Procedure B) P,,lP9,

Probability of acceptance at AQL

(Procedure BI

1) These relative samples are approximate only. The exact values are given in table D3 for each sample size code letter.

2) This acceptance number is only used in procedure A.

3) Acceptance of the lot is not permitted on the samples examined.

20

IS 2500 (Part 3) : 1995

IS0 2859-2 : 1992

Table D5 - Correspondence between lot sizes, AQL values in IS0 2669/l and LQ values

(Inspection levels I and II, procedure Bl

Lot size Use Sample

code letter11 size

AQL values in IS0 2959/l for limiting qualities lLQl2’

Li ng quality ILQI lmiti 1 : - 3,i! - j,(

- i - 8S - 1 12,5 20.0 32.0

2 to 90

91 to 150

151 to 280

281 to 500

501 to 1 200

1 201 to 3 200

3 201 to 10 000

10 001 to 35 000

35001 to 15Oooo

150061 t0500000

>500006

13

13

20

32

50

80

125

200

1

0.25

315

T

0.15 0.40

1500 0.10 0.25 0.40

800 0.15 0,25 0.65

1250

2000

1

1,065

),lO

1.10

+

I 4.0

2.5 6.5

4.0 6.5

4.0 10.0

t 6.5

4

I 1.5

‘I

1.0 2,5

1.5 2.5

1.5 4.0

t 2.5

,

1

0.65

t 0.40 1.0

0.65 1.0

0.65 1.5

l,O

re and sample size is determined by the inspection level. The sample size code letter to use is indicated by the

given inspection level, usually up one row for level I and down one row for level Il.

1) The correspondence between

head of the arrow corresponding

2’ When no AQL value appears in the table for a selected code letter and LQ value, an arrow will indicate that the sample size has to be increased if it

points downwards and decreased if it points upwards. The sample size and AQL value to be used correspond to the entrv at the head of the arrow

When thus sample size is greater than the lot size all items in the lot have to be inspected.

Table D6 - Correspondence between lot sizes and sample size code letters (Inspection levels S-l to S-4 and I to III, procedure B)

Lot size Special inspection levels General inspection levels

S-l and S-2 I s-3 I s-4 I I II I III

2 to 90 E E E E E F

91 to 150 E E E E F G

151 to 280 E E E E G H

281 to 500 E E E F H J

501 to 1200 E E F G J K

1201 to3200 E E G H K L

3 201 to 10 000 E F G J L M

10 001 to 35 000 E F H K M N

35001 to150000 E G J L N P

150001 to500000 E G J M P 0

>500000 E H K N Q R

NOTE - The sample size code letter indicates the appropriate row in table D5; it does not always indicate the sample size to be used directly since this

can depend on the limiting quality. Levels S-l and S-2, for example, give sample sizes independent of lot size but dependent on limiting quality.

ranging from 13 to 800.

21

Bureau of Indian Standards \

BIS is a statutory institution established under the Bureau of Indian Standards Act, 1986 to promote harmonious development of the activities of standardization, marking and quality ccrtifidtion of goods, and attending to connected matters in the country.

Copyright

BIS has the copyright of all its publications. No part of these publications may be reproduced in any form without the prior permission in writing of BIS. This does not preclude the free use, in the course of implementing the standard, of necessary details, such as symbols and sizes, type or grade designations. Enquiries relating to copyright be addressed to the Director (Publication), BIS.

Review of Indian Standards

Amendments are issued to standards as the need arises on the basis of comments. Standards are also reviewed periodically; a standard along with amendments is reaffirmed when such review indicates that no changes are needed; if the review indicates that changes are needed, it is taken up for revision. Users of Indian Standards should ascertain that they are in possession of the latest amendments or edition by referring to the latest issue of ‘BIS Handbook’ and ‘Standards Monthly Additions’.

This Indian Standard has been developed from Dot: No. MSD 3 (106)

Amend No.

Amendments Issued Since Publication

Date of Issue Text Affected

Headquarters: BUREAU OF INDIAN STANDARDS

Manak Bhavan, 9 Bahadur Shah Zafar Marg, New Delhi 110002 Telegrams: Manaksanstha Telephones: 323 0131,323 33 75,323 94 02 (Common to all offices)

Regional Offices: Telephone

*Central : Manak Bhavan, 9 Bahadur Shah Zafar Marg NEW DELHI 110002

Eastern :

Northern :

l/14 C.I.T. Scheme VII M, V.I.P. Road, Mnniktola CALCUTTA 700054

SC0 335-336, Sector 34-A, CHANDIGARH 160022

Southern : C.I.T. Campus, IV Cross Road, C!IENNAI 600113

Western :

Branches :

Manakalaya, E9 MIDC, Marol, Andheri (East) MUMBAI 400093

AHMADABAD. BANGALORE. BHGPAL. BHUBANESHWAR. COIMBATORE. FARIDABAD. GHAZIABAD. GUWAHATI. HYDERABAD. JAIP.UR. KANPUR. LUCKNOW. NAGPUR. PATNA. PUNE. THIRUVANANTHAPURAM.

323 76 17;323 38 41

{ 337 84 99,337 85 61 337 86 26,337 9120

{ 60 38 43 60 20 25

{ 235 02 16,235 04 42 235 15 19,235 23 15

{ 832 92 95,832 78 58 832 78 91,832 78 92

printed at Simco Printing Press, Delhi, India

is 2500-3 (1995): sampling inspection procedures, part 3:...

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